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Spatio-Temporal Networks: A GIS Perspective

Spatio-Temporal Networks: A GIS Perspective A Provocation at Visualizing Network Dynamics Workshop (11/4-6/2008) Supporting NATO Research Task Group IST-059/RTG-025.

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Spatio-Temporal Networks: A GIS Perspective

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  1. Spatio-Temporal Networks: A GIS Perspective A Provocation at Visualizing Network Dynamics Workshop (11/4-6/2008) Supporting NATO Research Task Group IST-059/RTG-025 Shashi ShekharMcKnight Distinguished Uninversity ProfessorUniversity of Minnesotawww.cs.umn.edu/~shekhar, www.spatial.cs.umn.edu OutlineBrief overview of my research groupRecent NGA NURI GrantNetwork Dynamics RepresentationProvocation: Time Aggregated Graphs

  2. Shortest Paths Storing graphs in disk blocks Evacutation Route Planning only in old plan Only in new plan In both plans Parallelize Range Queries Spatial Databases: Example Projects

  3. Location prediction: nesting sites Spatial outliers: sensor (#9) on I-35 Nest locations Distance to open water Vegetation durability Water depth Co-location Patterns Tele connections Spatial Data Mining: Example Projects

  4. 2. Journals GeoInformatica: An Intl. Journal on Advances in Computer Sc. for GIS Service Activities 1. Books Spatial Databases: A Tour, Prentice Hall, 2003 Encyclopedia of GIS, Springer, 2008

  5. Outline • Brief overview of my research • Recent NGA NURI Grant • Network Dynamics – Representations • Provocation: Time Aggregated Graphs

  6. Dynamic Purpose aware Graph Data Modelsfor Representing and Reasoning about Composite NetworksInvestigators: Shashi Shekhar,(U Minnesota) Start Date: August 2008 • Motivation: Complex and Fluid Spatio-temporal Structures • Challenge 1: Composite Networks • Challenge 2: Time-variant • Problem Definition • Inputs: (i) Complicated Feature datasets • A set of intelligence analysis tasks • Output: Data Model for representation and reasoning • Objective Function: Semantic expressiveness • Constraints:Computational resources

  7. Manhattan Money Laundering Incident Composite Networks • Example: • Money Laundering – ATM, Transportation (Road, Subway) • State of the Art: • Graph Theory • Time Geography: event-process • Network Engines • Critical Barriers: • Composite Multi-purpose networks • Time-variance • Approach: • Decompose composite networks into single purpose networks • Role ( network entities, e.g. bridge ) • is a bridge an obstacle or a link ? • Time aggregated graphs

  8. Adding Roles, Purposes to Network Data Model • Primitive Analysis Questions: • What is overall purpose of each component network? • What are network-element role-types (e.g. nodes, edges, obstacles, etc.) ? • What are instances of each element role-types? • What are the operations on element-types, roles, purposes and network? • Approach: Purpose Aware Graphs (PAG) • Tasks: • T1: Conceptual Model for PAG T2: Data types, Operators • T3: Query Processing algorithms T4:Purpose and Role Taxonomy • T5: Validation Proposed Extension Existing Graph model (Oracle)

  9. Syria's Suspected Nuclear Facility Source: New York Times and Digital Globe Challenge 2: Time-variant, Fluid Networks • Basic Modelling Questions: • What is the variation of the role of a node or an edge over time? • Where is a purpose changed or where does re-purposing occur? • What are the nodes and edges that causes the re-purposing of a network? • What are the nodes and edges that are part of a series of re-purposing? • Proposed Approach: • Dynamic-Purpose Aware Graphs (DPAG) • Tasks • G1: Event and Process Model for DPAG • G2: Data type, query operators on DPAG • G3: Algorithms for DPAG • G4: Storage and Access Methods for DPAG • G5: Validation

  10. Outline • Brief overview of my research • Recent NGA NURI Grant • Network Dynamics – Representations • Provocation: Time Aggregated Graphs

  11. 9 PM, November 19, 2007 Sensors on Minneapolis Highway Network periodically report time varying traffic 4 PM, November 19, 2007 7 PM, November 19, 2007 2) Crime Analysis Identification of frequent routes (i.e.) Journey to Crime 3) Dynamic Social Network Analysis Emerging leaders or dense sub-networks, Cells with increased chatter, 4) Knowledge discovery from Sensor data. Spreading Hotspots Motivation 1) Transportation network Routing • Delays at signals, turns, Varying Congestion Levels  travel time changes.

  12. Problem Definition • Input : a) A Spatial Network b) Temporal changes of the network topology and parameters. • Output : A model that supports efficient correct algorithms for computing the query results. • Objective : Minimize storage and computation costs. • Constraints : (i) Predictable future (ii) Changes occur at discrete instants of time, (iii) Logical & Physical independence,

  13. Key assumptions violated. • Ex., Prefix optimality of shortest paths • (greedy property behind Dijkstra’s algorithm..) Challenges in Representation • Conflicting Requirements • Expressive Power • Storage Efficiency • New and alternative semantics for common graph operations. • What is the best start time ? • Shortest Paths are time dependent. • Emerging, Dissipating, periodic, spreading, …

  14. N2 N2 N2 1 1 1 1 1 2 N4 N4 N5 N1 N5 N1 N4 N5 N1 2 2 2 2 2 2 N3 N3 N3 t=2 t=3 t=1 N2 N2 1 1 1 1 2 Node: N4 N5 N4 N1 N5 N1 2 2 Edge: 2 N3 N3 2 N.. t=4 t=5 Travel time Holdover Edge N1 N1 N1 N1 N1 N1 N1 N2 N2 N2 N2 N2 N2 N2 Transfer Edges N3 N3 N3 N3 N3 N3 N3 N4 N4 N4 N4 N4 N4 N4 N5 N5 N5 N5 N5 N5 N5 t=3 t=4 t=6 t=7 t=1 t=5 t=2 Related Work in Representation (1) Snapshot Model [Guting04] (2) Time Expanded Graph (TEG) [Kohler02, Ford65]

  15. High Storage Overhead Redundancy of nodes across time-frames Additional edges across time frames in TEG. Limitations of Related Work • Computationally expensive Algorithms • Increased Network size due to redundancy. • Inadequate support for modeling non-flow parameters on edges in TEG. • Lack of physical independence of data in TEG.

  16. Outline • Brief overview of my research • Recent NGA NURI Grant • Network Dynamics – Representations • Provocation • Representation: Time Aggregated Graphs • Example Analysis: Shortest Path

  17. N2 N2 N2 1 1 1 1 1 2 N4 N5 N4 N1 N5 N4 N1 N5 N1 2 2 2 2 2 2 N3 N3 N3 t=3 t=2 t=1 N.. N2 N2 1 Node: 1 1 1 N.. 2 N4 N5 N4 N1 N5 N1 Edge: Travel time 2 2 2 2 N3 N3 t=4 t=5 Proposed Approach Snapshots of a Network at t=1,2,3,4,5 Time Aggregated Graph • Attributes are aggregated over edges and nodes. N2 Node [,1,1,1,1] [1,1,1,1,1] [2,, , ,2] N4 N5 N1 Edge [m1,…..,(mT] [2,2,2,2,2] [2,2,2,2,2] N3 mi- travel time at t=i

  18. N : Set of nodes E : Set of edges T : Length of time interval nwi: Time dependent attribute on nodes for time instant i. ewi: Time dependent attribute on edges for time instant i. N2 [,1,1,1,1] On edge N4-N5 * [2,∞,∞,∞,2] is a time series of attribute; [1,1,1,1,1] [2,, , ,2] N4 N5 N1 * At t=1, the edge has an attribute value of 2. [2,2,2,2,2] [2,2,2,2,2] * At t=2, the ‘∞’ can indicate the absence of connectivity between the nodes at t=2. N3 Time Aggregated Graph [ew1,..,ewT ] | TAG = (N,E,T, [nw1…nwT ], nwi : N RT, ewi : E RT

  19. Performance Evaluation: Dataset Minneapolis CBD [1/2, 1, 2, 3 miles radii] • Road data • Mn/DOT basemap for MPLS CBD.

  20. (*) All edge and node parameters might not display time-dependence. (**) D. Sawitski, Implicit Maximization of Flows over Time, Technical Report (R:01276),University of Dortmund, 2004. TAG: Storage Cost Comparison • For a TAG of n nodes, m edges and time interval length T, • If there are k edge time series in the TAG , storage required for time series is O(kT). (*) • Storage requirement for TAG is O(n+m+kT) • For a Time Expanded Graph, • Storage requirement is O(nT) + O(n+m)T(**) • Experimental Evaluation • Storage cost of TAG is less than that of TEG if k << m. • TAG can benefit from time series compression.

  21. Outline • Brief overview of my research • Recent NGA NURI Grant • Network Dynamics – Representations • Provocation • Representation: Time Aggregated Graphs • Example Analysis: Shortest Path

  22. Routing Algorithms- Challenges • Violation of optimal prefix property • Not all optimal paths show optimal prefix property. • New and Alternate semantics • Termination of the algorithm: an infinite non-negative cycle over time

  23. N2 N2 N2 1 1 1 1 1 1 2 5 N4 N5 1 N1 N4 N5 N1 N4 N5 N1 2 2 2 2 2 2 N3 N3 N3 t=3 t=2 t=1 N2 N2 1 1 1 1 1 2 N4 N5 N4 N1 N5 N1 2 2 2 2 N3 N3 t=4 t=5 Challenges: Lack of Dynamic Programming Principle Find the shortest path travel time from N1 to N5 for start time t = 1. Naïve Solution: Reaches N5 at t=8. Total time = 7 N1 N2 N3 N4 N5 1 ∞ ∞ 1 ∞ ∞ 2 1 ∞ 2 ∞ 3 Optimal path: Reach N4 at t=3; Wait for t=4; Reach N5 at t=6 Total time = 5 3 3 2 3 1 ∞ 4 3 2 3 1 ∞ 5 3 2 3 1 8

  24. Challenge of Non-FIFO Travel Times Non-FIFO Travel times: • Arrivals at destination are not ordered by the start times. • Can occur due to delays at left turns, multiple lane traffic.. Different congestion levels in different lanes can lead to non-FIFO travel times. Signal delays at left turns cancause non-FIFO travel times. Pictures Courtesy: http://safety.transportation.org

  25. Dijkstra’s, A*…. Stationary Predictable Future Special case (FIFO) [Kanoulas07] Non-stationary LP, Label-correcting Alg. on TEG General Case Unpredictable Future [Orda91, Kohler02, Pallotino98] Routing Algorithms – Related Work SP-TAG, SP-TAG*,CapeCod Limitations: Label correcting algorithm over long time periods and large networks is computationally expensive. LP algorithms are costly.

  26. Start time = 1; Start node : N1 Iteration 1: N1_1 selected N1_2 = 2; N2_2 = 2; N3_3 = 3 Iteration 2: N2_2 selected N2_3 = 3; N4_3 = 3 Iteration 3: N3_3 selected N3_4 = 4; N4_5 = 5 . . . Iteration ..: N4_3 selected N4_4 = 4; N5_8 = 8 Iteration ..: N4_4 selected N4_5 = 5; N5_6 = 6 Related Work – Label Correcting Approach(*) • Selection of node to expand is random. • Algorithm terminates when no node gets updated. N1 N2 N3 N4 N5 t=8 t=3 t=4 t=6 t=7 t=2 t=1 t=5 • Implementation used the Two-Q version [O(n2T 3(n+m)] (*) Cherkassky 93,Zhan01, Ziliaskopoulos97

  27. N2 N2 [1,1,1,1,1] [1,1,1,1,1] [2,3,4,5,6] [2,3,4,5,6] [1,2,5,2,2] [2,4,8,6,7] N4 N5 N4 N5 N1 N1 [3,4,5,6,7] [2,2,2,2,2] [3,4,5,6,7] [2,2,2,2,2] N3 N3 N2 [2,3,4,5,6] [2,3,4,5,6] [2,4,6,6,7] N4 N5 N1 [3,4,5,6,7] [3,4,5,6,7] N3 Proposed Approach – Key Idea When start time is fixed, earliest arrival  least travel time (Shortest path) Arrival Time Series Transformation (ATST) the network: travel times  arrival times at end node  Min. arrival time series Result is a Stationary TAG. Greedy strategy (on cost of node, earliest arrival) works!!

  28. N2 N2 N2 1 1 1 1 1 2 N4 N5 N4 N1 N5 N4 N1 N5 N1 2 2 2 2 2 2 N3 N3 N3 t=3 t=2 t=1 N2 N2 1 1 1 1 2 N4 N5 N4 N1 N5 N1 2 2 2 2 N3 N3 Node: t=4 N.. t=5 Edge: Travel time Routing – New Semantics (Best Start Time) Finding the shortest path from N1 to N5.. Start at t=3: Start at t=1: Shortest Path is N1-N2-N4-N5; Travel time is 4 units. Shortest Path is N1-N3-N4-N5; Travel time is 6 units. Fixed Start Time Shortest Path Least Travel Time (Best Start Time) Shortest Path is dependent on start time!!

  29. Contributions (Broader Picture) • Time Aggregated Graph (TAG) • Routing Algorithms

  30. Selected Publications Time Aggregated Graphs • B. George, S. Shekhar, Time Aggregated Graphs for Modeling Spatio-temporal Networks-An Extended Abstract, Proceedings of Workshops (CoMoGIS) at International Conference on Conceptual Modeling, (ER2006) 2006. (Best Paper Award) • B. George, S. Kim, S. Shekhar, Spatio-temporal Network Databases and Routing Algorithms: A Summary of Results, Proceedings of International Symposium on Spatial and Temporal Databases (SSTD07), July, 2007. • B. George, J. Kang, S. Shekhar, STSG: A Data Model for Representation and Knowledge Discovery in Sensor Data, Proceedings of Workshop on Knowledge Discovery from Sensor data at the International Conference on Knowledge Discovery and Data Mining (KDD) Conference, August 2007. (Best Paper Award). • B. George, S. Shekhar, Modeling Spatio-temporal Network Computations: A Summary of Results, Proceedings of Second International Conference on GeoSpatial Semantics (GeoS2007), 2007. • B. George, S. Shekhar, Time Aggregated Graphs for Modeling Spatio-temporal Networks, Journal on Semantics of Data, Volume XI, Special issue of Selected papers from ER 2006, December 2007. • B. George, J. Kang, S. Shekhar, STSG: A Data Model for Representation and Knowledge Discovery in Sensor Data, Accepted for publication in Journal of Intelligent Data Analysis. • B. George, S. Shekhar, Routing Algorithms in Non-stationary Transportation Network, Proceedings of International Workshop on Computational Transportation Science, Dublin, Ireland, July, 2008. • B. George, S. Shekhar, S. Kim, Routing Algorithms in Spatio-temporal Databases, Transactions on Data and Knowledge Engineering (In submission). Evacuation Planning • Q Lu, B. George, S. Shekhar, Capacity Constrained Routing Algorithms for Evacuation Planning: A Summary of Results, Proceedings of International Symposium on Spatial and Temporal Databases (SSTD05), August, 2005. • S. Kim, B. George, S. Shekhar, Evacuation Route Planning: Scalable Algorithms, Proceedings of ACM International Symposium on Advances in Geographic Information Systems (ACMGIS07), November, 2007. • Q Lu, B. George, S. Shekhar, Capacity Constrained Routing Algorithms for Evacuation Planning, International Journal of Semantic Computing, Volume 1, No. 2, June 2007.

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